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A143508 G.f. satisfies: A(x) = 1 + x*A(x*A(x)^2)^2. 3
1, 1, 2, 9, 52, 372, 3058, 28074, 282028, 3059328, 35497672, 437499541, 5696752234, 78036803430, 1120687989348, 16823652188164, 263345788211608, 4289062071449610, 72543038644585822, 1271980596430351862, 23085579883157411532, 433071407705851089244 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..21.

FORMULA

Given g.f. A(x), let G(x) be defined by G(x*A(x)^2) = x, then

(1) G(x) = x/(1 + A(x)^2*G(x))^2,

(2) A(G(x)) = 1 + A(x)^2*G(x).

EXAMPLE

G.f. A(x) = 1 + x + 2*x^2 + 9*x^3 + 52*x^4 + 372*x^5 + 3058*x^6 +...

A(x)^2 = 1 + 2*x + 5*x^2 + 22*x^3 + 126*x^4 + 884*x^5 + 7149*x^6 +...

A(x*A(x)^2) = 1 + x + 4*x^2 + 22*x^3 + 156*x^4 + 1285*x^5 + 11886*x^6 +...

A(x*A(x)^2)^2 = 1 + 2*x + 9*x^2 + 52*x^3 + 372*x^4 + 3058*x^5 +...

Define G(x) by G(x*A(x)^2) = x, then

G(x) = x - 2*x^2 + 3*x^3 - 12*x^4 + 17*x^5 - 198*x^6 - 345*x^7 +...

such that G(x) = x/(1 + A(x)^2*G(x))^2.

PROG

(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A^2, x, x*A^2)); polcoeff(A, n)}

CROSSREFS

Cf. A212029, A143501.

Sequence in context: A305987 A231494 A006152 * A052882 A248440 A330200

Adjacent sequences:  A143505 A143506 A143507 * A143509 A143510 A143511

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Aug 21 2008

STATUS

approved

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Last modified October 26 08:00 EDT 2021. Contains 348267 sequences. (Running on oeis4.)